1. Field of the Invention
A method for the determination of the static corrections to be applied to shear-wave reflection data in the presence of shear-wave anisotropy in the near-surface earth material.
2. Discussion of Related Art
Seismic exploration is a method for acoustically measuring and displaying the topography of one or more subsurface earth layers of interest along a selected line of survey. Typically a sound source creates an acoustic wavefield at or near the surface of the earth. Certain of the wavefield components propagate downwardly into the earth whence they are reflected back to the surface from various subsurface earth layers. Other components are refracted along the various interfaces between earth layers. Yet other wavefield components propagate directly along the surface of the earth or just beneath the surface. The returning direct, reflected and refracted acoustic signals are sensed by each of a plurality of suitable spaced-apart seismic sensors emplaced at or near the surface of the earth along the line of survey at selected stations. The sensors convert the acoustic signals to electrical signals that may be transmitted to a storage/computer means for later processing and display. The processed seismic data harvested along each line of survey are presented as a display of a plurality of time-scale traces laterally spaced apart in accordance with the sensor spacing. From a plurality of intersecting lines of survey, a detailed multi-dimensional topographic map of one or more targeted subsurface formations can be displayed.
A seismic source for land use may be a small explosive or impactive device triggered at or near the surface of the earth or the source may be a vibrator. Explosive or impactive devices radiate an essentially non-polarized, omni-directional wavefield including troublesome boundary or Rayleigh waves. A vibrator injects a chirp signal into the ground. The vibrator can be designed to produce compressional (P) waves, horizontally polarized shear (SH) waves or vertically polarized (SV) shear waves.
P waves vibrate in-line with the direction of propagation. SH waves vibrate transversely and horizontally with respect to the propagation direction. SV waves, as the name implies, vibrate vertically with respect to the direction of propagation. Rayleigh waves propagate along the air-earth interface as boundary waves having an elliptical retrograde mode in the presence of an earth layer whose velocity increases with depth.
In seismic surveying, the desired wave types are usually P-waves and S-waves. The frequency content may be on the order of 10 to 100 Hz. Rayleigh waves, on the other hand are very low-frequency, one to 30 Hertz or less, high-amplitude events which seriously mask the early-arriving reflected events. Geophysicists traditionally go to great lengths to eliminate or at least minimize the generation of Rayleigh waves, also known as ground roll, which are considered to be useless trash signals. Methods used to eradicate Rayleigh waves include carefully-designed spatial and instrumental filtering regimes during data acquisition and sophisticated data-processing techniques during the data interpretation phase.
In terms of velocities, P waves most commonly range from about 1450 meters per second (m/s) for water to as much as 5000 m/s for competent formation layers although extreme values of 8 km/s have been encountered for deep crustal layers. In the weathered layer near the surface, P-waves may have a velocity as low as 500 m/s. Shear waves have a velocity of about half the corresponding P wave velocity. Shear waves can not propagate in fluids. The velocity of Rayleigh waves may be about 0.8 to 0.9 that of the corresponding shear-waves but can never equal or exceed the shear wave velocity.
Throughout this disclosure, the term "velocity" means the velocity of propagation of an acoustic wave through a medium under consideration. If that term is used in any other sense, it will be so defined.
Some rock types are isotropic, exhibiting the same velocity in all directions. Other rock types, those that are well stratified or that are characterized by distinct fracture planes, are anisotropic such that their velocity is azimuth dependent.
A shear-wave seismic survey is particularly useful in the diagnosis of vertical fracture plane orientation by analyzing the anisotropic effect due to formation fracture planes, a matter that is important in establishing the azimuthal alignment of a deviated borehole for use in oil and gas recovery. See for example U.S. Pat. No. 4,817,061, issued Mar. 28, 1989 to R. M. Alford et al. wherein a shear-wave-survey method is disclosed which, in one embodiment, may be carried out by using differently polarized shear waves along a common line of profile. Two different sets of data are collected, one set for each polarization direction. A first data set is provided by imparting shear wave energy into the earth by a shear wave seismic source polarized in a first direction along a seismic line of profile, to be received by a first sensor having matched polarization. A second data set is provided by imparting shear wave energy into the earth by a shear wave seismic source polarized in a second direction along the seismic line of survey and received by a second sensor having matched polarization. A first and a second sensor may be co-located at each station. A conventional P-wave reflection survey may accompany the shear-wave survey. The survey results derived from the respective sets of data are processed, separately displayed and compared; any differences between the displays constitute a measure of fracture orientation and density. According to Alford, subsurface zones of high fracture density, once identified have been found to afford a higher likelihood of successful oil well completion.
In addition to oil exploration, shear-wave analyses of the velocity of the near surface material are useful in engineering studies to determine the load-bearing distribution characteristics of the soil using Poisson's ratio, .sigma., which is given by EQU .sigma.=(R.sup.2 -2)/2(R.sup.2 -1), (1)
where R =V.sub.p /V.sub.s, V.sub.p is the P-wave velocity and V.sub.s is the shear wave velocity of the near surface material. Assuming that the earth consists of alternating thin layers of elastic material between layers of an inelastic material, the vertical stress, q, at some depth, z, at a radial distance, r, from the point of application of a concentrated load, Q, may be estimated from ##EQU1## where
a=(1-2.sigma.), and PA1 b=(2-2.sigma.). PA1 c=group velocity of boundary wave, PA1 V.sub.0 =phase velocity of direct compressional wave, PA1 V.sub.s.theta. =low-velocity layer shear wave vector.
Reflection data of all types, whether P-wave or S-wave, must be corrected for the irregular time delays (also known as statics or static corrections) through the near-surface weathered layer as will now be explained.
Please refer to FIG. 1. A surface source 10 radiates a wavefield into the earth which propagates to sensors 12 and 14 emplaced on the surface 16 (air-earth interface) of the earth. One source and two sensors are shown but several sources may be used in tandem and several hundred spaced-apart sensors may be deployed along a line of survey in the real world. In a stratified earth, layer V.sub.0 sandwiched between interfaces 16 and 18 is the low velocity, weathered layer or LVL. Layer V.sub.1 might have a P-wave velocity of 2150 m/s while the layer beneath interface 18 at some depth Z might indicate a P-wave velocity of about 3000 m/s. The respective shear wave velocities would be about half the above values.
In FIG. 1, ray segments 22, 23, 24, 25 represent the trajectory of a wave field from source 10 to sensor 12 after reflection from interface 20. Ray segments 26-29 show the wavefield trajectory from source 10 to sensor 14. Refracted energy propagates along segments 30,32 and 34 to sensor 12 and along segments 30, 32, 33 and 35 to sensor 14. For distances less than the critical distance, the seismic signals arriving first will travel via a direct path 36 to a sensor such as 12. Beyond the critical distance, the refracted arrivals from the base of the LVL will appear first because of their shorter travel time due to refraction along interface 18. Rayleigh or boundary waves travel along segments 38 and 39 to sensors 12 and 14 respectively at the air-earth interface 16 in an elliptical retrograde mode as shown by ellipse 40.
Energy traveling to sensor 12 after reflection from interface 20 is retarded by passage through the LVL over segments 22 and 25 at velocity V.sub.0. Similarly for energy traveling to sensor 14 via segments 26 and 29. If the LVL thickness is uniform and V.sub.0 does not change laterally, the time delay will be the same at both sensors. If, on the other hand, there is a thickness difference as in FIG. 2, after correction for angularity (NMO) the travel times for a reflection from a flat interface as seen by two spaced-apart sensors such as 12 and 14, will show a false time differential due to a greater thickness of LVL beneath sensor 12. As earlier stated, the required compensatory time corrections are known as static corrections or simply statics.
A classical method for evaluating static corrections is taught by U.S. Pat. No. 2,087,120 issued Jul. 13, 1937 to H. Salvatori et al. In that method, the distance between the source and a sensor such as 12 is divided by the formation velocity, V.sub.1, to yield the travel time over refracted travel path 32 to sensor 12 along interface 18. That time is subtracted from the total observed refracted travel time. The remainder is the total static delay time At through the LVL. The slight error due to use of an assumed vertical path vs. the actual slant paths such as 22 and 25 is usually not significant for the velocity relationships ordinarily encountered. Statics for sensor 14 are calculated similarly. The statics applicable to each sensor are subtracted from the total reflection travel time seen by that sensor. The reflection travel time, corrected for NMO and statics, is then extrapolated to an arbitrary reference surface, using some pre-selected replacement velocity V.sub.r to account for elevation differences.
U.S. Pat. No. 4,577,298, issued Mar. 18, 1986 to David Hinkley, teaches a more sophisticated method for applying surface consistent statics to seismic traces. Measurements based on the time of arrival of reflection and refraction signal components in a trace gather are used to produce source-receiver statics estimates which are used in turn to correctly time-shift the individual traces of the gather for subsequent common depth point stacking.
In another commercial method, the residual statics are determined by cross correlation between the seismic traces as described by Ralph Wiggins in Residual Static Correction Analysis as a General Linear Inverse Problem, published in Geophysics, v. 41, n. 5, 1976.
D. H. Rothman, in Non-linear Inversion, Statistical Mechanics and Residual Statics Estimation, published in Geophysics, v. 50, n. 12, 1985, describes a Monte Carlo statistical method for obtaining static corrections.
It is of interest that all of those prior art methods apply to P-wave reflection profiling.
As is well known, velocity V.sub.0 is usually either estimated or is measured with the aid of special weathering shots. The velocity so determined is a P-wave velocity. During data processing, an arbitrary, substantially constant value is selected for V.sub.0 which is used to calculate statics at the respective sensor and source locations within a given region but without regard to the azimuth of the line of survey or to whether P-wave or S-wave data are to be processed because the LVL was, for simplicity, considered to be amorphous and isotropic.
I have discovered that the LVL is anisotropic. To prevent data misties between co-located shear wave sensors having mutually perpendicular polarizations, the static corrections must be determined using an LVL shear-wave velocity vector appropriate to the polarization directions of the individual sensors. Because the shear wave velocity attributable solely to the LVL cannot be straightforwardly measured directly, there is a need for a method for deriving that quantity indirectly.